Answer to Question #144099 in Analytic Geometry for Bonevie tutor

Question

The cables of a suspension bridge are in the shape of parabola. The towers supporting the cables are 800 ft apart and 100 ft high. If cables touch the road surface midway between the towers, what is the hieght of the cable at a point 200 feet from the middles of the bridge?

Answer 1

AB = 800 ft , AC=BD= 100 ft , HK - ?

cabels have equation $y=kx^2$

D(400, 100) belongs to the graph $y=kx^2$

$100 = k*400^2$

$k = 1/1600$

$y = 1/1600 *x^2$

H(200, a) when $a = 1/1600*200^2 = 40000/1600 = 25$

HK = 25 ft

answer : 25 ft